CBSE Boardहिन्दी माध्यमकक्षा 12 साइन्सगणितसमाकलन2 Marks
Question
$\int \sqrt{x^{2}+2 x+5} d x$ ज्ञात कीजिए।
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Answer
ध्यान दीजिए कि $\int \sqrt{x^{2}+2 x+5} d x$ $=\int \sqrt{(x+1)^{2}+4} d x$ अब x + 1 = y रखने पर dx = dy, तब $\int \sqrt{x^{2}+2 x+5} d x$ $=\int \sqrt{y^{2}+2^{2}} d y $ $=\frac{1}{2} y \sqrt{y^{2}+4}$ $+\frac{4}{2} \log \left|y+\sqrt{y^{2}+4}\right|$ + C $=\frac{1}{2}(x+1)$ $ \sqrt{x^{2}+2 x+5}$$+2 \log \left|x+1+\sqrt{x^{2}+2 x+5}\right|$ + C
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